CFA Level I — Fixed Income Cheatsheet
2025 Curriculum · Volume 6 · 19 Learning Modules

LM1–2 Features & Flows
LM3–5 Markets
LM6–8 Valuation & Yields
LM9–13 Risk & Duration
LM14–19 Credit & ABS

LM 1–2 — Bond Features, Cash Flows & Types
LM1Fixed-Income Instrument Features
  • Issuer: sovereign, corporate, SPE, supranational — determines credit risk
  • Maturity: money market (<1 yr), capital market (≥1 yr); perpetual = no maturity
  • Par (face) value: principal repaid at maturity; coupon calculated on par
  • Coupon rate: fixed, floating (MRR + spread), zero-coupon, step-up
  • FRN coupon: Market Reference Rate (MRR) + issuer-specific spread
  • Seniority: Senior secured > Senior unsecured > Subordinated (junior)
  • Pari passu: “equal footing” — same seniority as other senior debt
  • Price and yield move inversely; higher credit risk → higher required yield
Annual coupon = Coupon rate × Par value. Bond price = PV of all future cash flows discounted at the market discount rate.

LM1Indentures & Covenants
  • Indenture (trust deed): legal contract describing all bond terms
  • Affirmative covenants: actions issuer must take (make payments, maintain insurance, comply with laws)
  • Negative covenants: restrictions on issuer (limits on debt, asset sales, dividends, liens)
  • Covenants protect bondholders; more restrictive = lower credit risk = lower yield
  • Cross-default: default on one obligation triggers default on all
  • Change-of-control put: bondholder can sell back if company acquired
LM2Cash Flow Structures
Bullet bondPeriodic coupon; full principal at maturity
Amortizing bondPrincipal repaid over life (e.g., mortgage)
Sinking fundIssuer retires portion of principal on schedule
Zero-couponNo coupons; issued at discount; pure discount bond
Deferred couponNo coupons initially; payments begin later

LM2Contingency Provisions
Callable bondIssuer can redeem early; benefits issuer
Putable bondInvestor can sell back early; benefits investor
Convertible bondBondholder can convert to equity shares
  • Callable: issuer calls when rates fall (refinance cheaper); yield > comparable non-callable
  • Putable: investor puts when rates rise (reinvest at higher rate); yield < comparable non-putable
  • Convertible: conversion ratio = par / conversion price; lower yield (equity upside)
  • Call protection period: issuer cannot call during this initial period
LM2Legal & Tax Considerations
  • Domestic bonds: issued in home country, home currency
  • Foreign bonds: issued in another country’s market and currency (e.g., Yankee, Samurai, Bulldog)
  • Eurobonds: issued in a currency different from the country where sold
  • Global bonds: issued in domestic + Eurobond markets simultaneously
  • Tax: coupon interest taxed as ordinary income; capital gains may differ
  • Zero-coupon bonds: imputed interest taxable annually even without cash flow
  • Tax-exempt bonds (e.g., US municipal): lower pre-tax yield but may be higher after-tax

LM 3–5 — Fixed-Income Markets: Issuance & Trading
LM3Market Segments & Trading
Market Segments
SovereignGovernment bonds (T-bills, T-notes, T-bonds)
CorporateIG and HY; largest non-sovereign sector
SecuritizedABS, MBS, CLOs; backed by asset pools
MunicipalLocal governments; often tax-exempt
Primary vs. Secondary
  • Primary: new issuance — public offering (underwritten) or private placement
  • Secondary: existing bonds — mostly OTC dealer markets (not exchanges)
  • Fixed-income indexes: Bloomberg Aggregate, ICE BofA; criteria include currency, maturity, credit quality
LM4–5Corporate & Government Issuers
Short-Term Corporate Funding
Commercial paper (CP)Unsecured; ≤270 days; discount basis
Bank loansBilateral or syndicated; floating rate
RepoSell security + agree to repurchase; short-term funding
  • Repo rate depends on collateral quality, term, and credit of counterparty
  • Haircut: overcollateralization to protect lender; higher for riskier collateral
Government Issuers
  • Sovereign debt: backed by taxation power; benchmark for other issuers
  • On-the-run: most recently issued; most liquid; benchmark yield
  • Off-the-run: previously issued; less liquid; higher yield
  • Non-sovereign: states, provinces, municipalities; varying credit quality
  • Supranational: World Bank, IMF; usually high-quality

LM 6 — Bond Valuation: Prices & Yields
PricingBond Price Calculation
PV = PMT/(1+r)1 + PMT/(1+r)2 + … + (PMT+FV)/(1+r)N
  • r = market discount rate (required yield) per period
  • If coupon rate > market rate → premium (price > par)
  • If coupon rate < market rate → discount (price < par)
  • If coupon rate = market rate → par (price = 100)
  • Premium/discount amortizes toward par as maturity approaches (“pull to par”)
Flat vs. Full Price
  • Full (dirty) price: PV of future cash flows = flat price + accrued interest
  • Flat (clean) price: quoted price; excludes accrued interest
  • Accrued interest: coupon earned since last payment date but not yet paid
  • Day-count: actual/actual (government) or 30/360 (corporate)
YTMYield-to-Maturity & Price Relationships
  • YTM: single discount rate that equates PV of cash flows to market price; IRR of bond
  • YTM assumes: held to maturity, no default, coupons reinvested at YTM
  • YTM is an annualized measure; must convert from per-period rate
Price–Yield Properties
  • Inverse: price and yield move in opposite directions
  • Convexity: price–yield curve is convex (bowed toward origin)
  • Coupon effect: lower coupon = more price sensitivity to yield changes
  • Maturity effect: longer maturity = more price sensitivity (usually)
  • Price increase for yield decrease > price decrease for same yield increase (convexity)
Matrix Pricing
  • Estimates yield for illiquid/infrequently traded bonds using comparable bonds
  • Interpolate yield from bonds with similar credit quality and maturity

LM 7–8 — Yield & Yield Spread Measures
LM7Fixed-Rate Bond Yields
Periodicity & Conversion
  • Periodicity = number of coupon payments per year (1 = annual, 2 = semiannual)
  • To compare yields with different periodicities, convert to common basis
(1 + APRm/m)m = (1 + APRn/n)n
Other Yield Measures
Current yieldAnnual coupon / flat price
Yield-to-call (YTC)YTM assuming call at first call date
Yield-to-worst (YTW)Lowest of YTM, YTC at all call dates
Option-adjusted yieldYTM adjusted for value of embedded option
Callable bond: YTW = min(YTM, all YTCs). Callable → OAS < Z-spread.

LM7–8Yield Spreads & FRN Measures
Spread Measures
G-spreadYield − government benchmark yield (same maturity)
I-spreadYield − swap rate (SOFR, EURIBOR-based)
Z-spread (zero-volatility)Constant spread added to each spot rate
OASZ-spread minus option value; used for callable/putable
Floating-Rate Notes
  • FRN coupon resets periodically: MRR + quoted margin (spread)
  • Discount margin (DM): required spread over MRR that prices FRN at par at reset
  • If DM > quoted margin → FRN priced below par (credit deteriorated)
  • If DM < quoted margin → FRN priced above par (credit improved)
Money Market Yields
  • Quoted on discount basis (T-bills) or add-on basis (bank deposits, CP)
  • Discount rate ≠ add-on rate; convert for comparison

LM 9 — Term Structure: Spot, Par & Forward Curves
SpotSpot Rates & Curve
  • Spot rate: yield on a zero-coupon bond for a given maturity
  • Discount each cash flow at the corresponding spot rate → no-arbitrage price
  • Spot curve = plot of spot rates vs. maturity
  • More precise than using a single YTM for all cash flows
PV = C/(1+z1) + C/(1+z2)2 + … + (C+FV)/(1+zN)N

ParPar Rates
  • Par rate: coupon rate that prices a bond at par using spot rates
  • Derived from spot rates via bootstrapping
  • Upward-sloping spot curve → par rates < spot rates
  • Downward-sloping spot curve → par rates > spot rates
  • Par curve is used for benchmark government yield curves
ForwardForward Rates
  • Forward rate: implied future rate derived from spot rates
  • Notation: f(j,k) = rate starting in j periods for k periods
  • Breakeven reinvestment rate: makes investor indifferent between strategies
  • Upward-sloping spot → forward > spot; downward-sloping → forward < spot
(1+z2)2 = (1+z1)(1+f(1,1))
Forward rates are marginal returns for extending maturity by one period.

LM 10–13 — Interest Rate Risk, Duration & Convexity
LM10Sources of Return & Interest Rate Risk
1Coupons + Principal
+
2Reinvestment Income
+
3Price Gain/Loss

  • Reinvestment risk: coupons reinvested at lower rates when rates fall
  • Price risk: bond price falls when rates rise (if sold before maturity)
  • Reinvestment risk and price risk have an inverse relationship
  • Longer horizon → reinvestment risk dominates; shorter → price risk dominates
  • If investment horizon = Macaulay duration → risks exactly offset
Realized return = YTM only if: held to maturity, no default, coupons reinvested at YTM.

LM10–11Duration Measures
Macaulay durationWeighted-avg time to receipt of cash flows (in years)
Modified durationMacDur / (1 + YTM/n); % price change per 1% yield
Approx. ModDur(PV− − PV+) / (2 × Δyield × PV0)
Money durationModDur × Market value of bond position
PVBP(PV− − PV+) / 2; price change per 1 bp
%ΔPVFull ≈ −ModDur × ΔYield
Duration is a linear approximation — works well for small yield changes.

LM12Convexity & Portfolio Measures
  • Convexity: measures curvature of the price–yield relationship
  • Convexity adjustment improves duration estimate for large yield changes
  • Higher convexity = greater price gain for yield decrease, smaller loss for increase
  • Investors prefer higher convexity (pay higher price / accept lower yield)
%ΔPVFull ≈ −ModDur × ΔYield + ½ × Convexity × (ΔYield)2
Portfolio Measures
  • Portfolio duration = weighted average of individual bond durations
  • Portfolio convexity = weighted average of individual convexities
  • Assumes parallel shift in yield curve (all yields change by same amount)
LM11–13Duration Properties & Curve Measures
Duration Properties
  • Longer maturity → higher duration (more price sensitivity)
  • Lower coupon → higher duration (more weight on final cash flow)
  • Lower yield → higher duration (PV of distant cash flows increases)
  • Zero-coupon bond: MacDur = maturity; highest duration for given maturity
  • FRN: duration ≈ time to next reset (very low interest rate risk)
Curve-Based Measures (LM13)
Effective durationCurve-based; used for bonds with embedded options
Key rate durationSensitivity to shift at single maturity point on curve
Empirical durationRegression-based; actual price–yield sensitivity
Effective duration captures option effects; yield duration does not.

LM 14–16 — Credit Risk & Credit Analysis
LM14Credit Risk Components
Expected loss = Probability of default × Loss given default
  • Probability of default (PD): likelihood issuer fails to pay
  • Loss given default (LGD): 1 − recovery rate; loss if default occurs
  • Recovery rate: % of par recovered after default; varies by seniority
  • Credit risk sources: macro conditions, financing mismatch, issuer-specific
  • Credit spread = yield − benchmark risk-free rate; widens when risk rises
Credit Ratings
Investment grade (IG)BBB− / Baa3 and above
High yield (HY)BB+ / Ba1 and below
Rating agenciesS&P, Moody’s, Fitch
Ratings can lag market pricing; fallen angels = IG downgraded to HY.

LM14Yield Spread Factors
Macroeconomic Factors
  • Spreads widen in recession/crisis; narrow in expansion
  • Credit cycle: spreads tighten in good times → underpriced risk → widening
Market Factors
  • Liquidity: less liquid bonds → wider spreads
  • Supply/demand imbalances affect spread levels
Issuer-Specific
  • Leverage, coverage ratios, cash flow stability, industry risk
  • Spread impact on returns: %ΔPrice ≈ −ModDur × ΔSpread
LM15–16Government & Corporate Analysis
  • Sovereign: institutional strength, fiscal policy, external balance, monetary flexibility
  • Corporate: industry, competitive position, governance + leverage, coverage, cash flow ratios
  • Secured > unsecured; senior > subordinated; higher recovery for secured
  • Notching: issue rating may differ from issuer rating based on seniority

LM 17–19 — Securitization, ABS & MBS
LM17Securitization Process
1Originator creates loans
→
2Sells to SPE
→
3SPE issues ABS to investors

  • SPE (Special Purpose Entity): bankruptcy-remote; isolates assets from originator
  • Servicer: collects payments from borrowers; passes to SPE / trustee
  • Benefits to issuer: removes assets from balance sheet; lower funding cost; frees capital
  • Benefits to investor: access to diversified asset pools; tailored risk/return tranches
LM18ABS Credit Enhancement
OvercollateralizationCollateral value > ABS value issued
Subordination (tranching)Junior tranche absorbs losses first
Reserve fundCash set aside to cover shortfalls
Excess spreadPool interest income > payments to ABS holders
External: surety bond / LOCThird-party guarantee of payments

LM18–19ABS Types & MBS
Non-Mortgage ABS
Credit card ABSRevolving; non-amortizing; lockout period
Auto loan ABSAmortizing; prepayment risk exists but limited
CLOPool of leveraged loans; senior + mezzanine + equity tranches
Covered bondsDual recourse: issuer + cover pool; stay on balance sheet
Mortgage-Backed Securities (LM19)
  • Pass-through: pro-rata share of mortgage pool payments; subject to prepayment
  • CMO: tranches from pass-throughs; redistribute prepayment risk (time tranching)
  • Prepayment risk: contraction (faster) + extension (slower) risk
  • Contraction risk: rates fall → borrowers refinance → early principal return
  • Extension risk: rates rise → fewer refinances → cash flows slow down
  • WAL (weighted average life): better than contractual maturity for MBS
  • Agency RMBS (Ginnie Mae, Fannie, Freddie): government-backed; lower credit risk
  • CMBS: commercial mortgages; balloon risk; call protection via lockout/defeasance

High-Frequency Exam Traps & Quick Reference
Key Distinctions (frequently tested)
Flat vs. full priceFull = flat + accrued interest
G-spread vs. Z-spreadG = single benchmark; Z = added to each spot rate
Z-spread vs. OASOAS = Z-spread minus option cost
Macaulay vs. modified dur.MacDur = years; ModDur = % price change per 1% yield
Yield vs. curve durationYield = change in own YTM; curve = benchmark shift
Contraction vs. extensionContraction = faster prepay; extension = slower
Agency vs. non-agency MBSAgency = govt-backed; non-agency = private; more credit risk
Callable vs. putableCall benefits issuer (higher yield); put benefits investor (lower yield)
Covered bond vs. ABSCovered: dual recourse, on balance sheet; ABS: sold to SPE
On-the-run vs. off-the-runOn-the-run = newest, most liquid, benchmark

Key Formulas & Numbers
Bond pricePV = Σ CFt / (1+r)t
ModDurMacDur / (1 + YTM/n)
%ΔPrice (duration only)≈ −ModDur × ΔYield
%ΔPrice (with convexity)≈ −ModDur × ΔY + ½ Conv × ΔY2
Expected lossPD × LGD
LGD1 − Recovery rate
Forward rate(1+zn)n = (1+zj)j(1+f)k
IG thresholdBBB− / Baa3 and above
Zero-coupon MacDur= Maturity (always)
FRN duration≈ Time to next reset (very low)

Remember: Price and yield move inversely. Duration measures price sensitivity to yield changes — longer maturity, lower coupon, and lower yield all increase duration. Convexity improves the duration estimate for large yield changes. Credit spreads widen in stress and narrow in calm. For bonds with embedded options, use effective (curve-based) duration and OAS, not yield-based measures. Securitization creates bankruptcy-remote SPEs; MBS carry prepayment risk (contraction + extension).